A100062 Denominator of the probability that an integer n occurs in the cumulative sums of the decimal digits of a random real number between 0 and 1.

9, 81, 729, 6561, 59049, 531441, 4782969, 43046721, 387420489, 3486784401, 31381059609, 282429536481, 2541865828329, 22876792454961, 205891132094649, 1853020188851841, 16677181699666569, 150094635296999121

Offset: 1

Author

Eric W. Weisstein, Nov 01 2004

Keywords

• nonn
• base
• frac

Comments

Essentially the same as A001019 = powers of 9.

Also number of n-digit positive integers with no identical adjacent digits. Hence the numerator (with A052268 as denominator) of the probability that an n-digit positive integer has this property (e.g., 9/9, 81/90, 729/900, ..., where A100062(n)/A052268(n) reduces to A001019(n-1)/A011557(n-1)). - Rick L. Shepherd, Jun 08 2008

Examples

			1/9, 10/81, 100/729, 1000/6561, 10000/59049, ...
		

Links

• Stanislav Sykora, Table of n, a(n) for n = 1..666; previous Table by Rick L. Shepherd went up to n=30.
• Tanya Khovanova, Recursive Sequences
• Eric Weisstein's World of Mathematics, Evil Number
• Index entries for linear recurrences with constant coefficients, signature (9).

Crossrefs

Cf. A001019, A011557 A052268, A100061, A100062, A271880, A271881.

Programs

Magma

[9^n : n in [1..30]]; // Wesley Ivan Hurt, Apr 18 2016

Maple

A100062:=n->9^n: seq(A100062(n), n=1..30); # Wesley Ivan Hurt, Apr 18 2016

Mathematica

9^Range[20] (* Harvey P. Dale, Dec 25 2012 *)

PARI

\\ The 'old' approach, using the generating function:
s = Vec(Ser((1-x^9)/(x^10-10*x+9),x,666));
a = vector(#s,n,denominator(s[n])) \\ Stanislav Sykora, Apr 16 2016

Formula

a(n) = 9^n. - Max Alekseyev, Mar 03 2007

From Philippe Deléham, Nov 23 2008: (Start)

a(n) = 9*a(n-1), n>1; a(1)=9.

G.f.: 9x/(1-9x). (End)

a(n) = A001019(n) for n>0. - Wesley Ivan Hurt, Apr 18 2016

Extensions

More terms from Rick L. Shepherd, Jun 08 2008